J. Micromech. Microeng. 9 (1999) 236–244. Printed in the UK PII: S0960-1317(99)00878-5 On the buckling behavior of micromachined beams Weileun Fang, Chun-Hsien Lee and Hsin-Hua Hu Power Mechanical Engineering Department, National Tsing Hwa University, Hsinchu, Taiwan Received 12 January 1999 Abstract. Thin film materials are normally under residual stresses as a result of fabrication processes. Unlike microelectronics devices, a micromechanical structure is no longer constrained by its underlying silicon substrate after anisotropic etch undercutting; therefore, residual stresses may result in the bending and buckling of a micromechanical structure. The buckling behavior has been exploited to measure the residual stresses of thin films. This characteristic can also be applied to fabricate out-of-plane three-dimensional micromechanical structures if their deflections are controllable. The buckling of a microbridge is difficult to predict since it is strongly dominated by its fabrication processes and boundary conditions. Currently the information regarding the buckling of micromachined structures is still not complete. The application of the buckling behavior is therefore limited. In this research, the effects of boundary conditions and gradient residual stresses on the buckling behavior of microbridges were studied using analytical and experimental approaches. The variations of the buckling amplitude orientations with the thickness and length of the microbridges were obtained; therefore, the buckling behavior can be predicted and then exploited to fabricate useful micromechanical structures. The potential application of this research lies in preventing the leakage of the microvalves. 1. Introduction As the result of fabrication processes, thin film materials are normally under residual stresses [1]. The residual stresses may lead to unwanted deformation, such as bending, buckling and twisting towards micromachined structures which are no longer constrained by the silicon substrate underneath after undercutting, as illustrated in figure 1. The deformation of micromachined structures can be used to determine the residual stresses of thin films [1–3]. The residual stresses can also be exploited to fabricate mechanical structures with desired configurations, especially the structures with out- of-plane deformation. A real three-dimensional structure can therefore be fabricated through the micromachining technology. The applications of this approach are the predeformed microvalve plates in microfluidic systems [4]. Microcantilevers and microbridges (or in terms of clamped–clamped beams) shown in figure 1 are two fundamental predeformed mechanical structures. In general, the bending effect predeforms the cantilever, which contains one fixed end and one free end, as indicated in figure 1(a). On the other hand, the buckling effect predeforms the microbridge, which contains two fixed ends, as indicated in figure 1(b). The mechanical behaviors of cantilevers have recently been studied extensively [5, 6] and well understood; however, the information regarding the buckling behavior of micromachined structures is still limited [7–9]. This is mainly due to the difficulties of predicting the elastic instability phenomena of the buckling behavior. For instance, Figure 1. Out-of-plane deformation of: (a) microcantilever; and (b) microbridge. the buckling of a microbridge could be affected by thin film residual stresses, fabrication processes, as well as boundary conditions. In fact, most of the models still considered the buckling behavior as a linear perfect case [8, 9]. Though the imperfection effect during buckling was mentioned in [7], the sources that may introduce imperfections were not discussed. The applications of predeformed microbridges are thus limited. The goal of this research is to develop a model regarding the imperfections of a microbridge during buckling. The unsymmetric and flexible boundaries of the microbridges and the gradient residual stress are considered as two major sources of imperfections in the proposed approach. The buckling behavior of the microbridges observed in the experiment can be explained qualitatively by using a study of the boundary and residual stress. 0960-1317/99/030236+09$30.00 © 1999 IOP Publishing Ltd
On the buckling behavior of micromachined beams
Jun 14, 2023
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